The ripples in a certain groove 12.7 cm from the center of a 33-rpm phonograph record have a wavelength of 1.75 mm. What will be the frequency of the sound emitted?

The frequency of the sound emitted can be calculated using the equation f = v/λ, where f is the frequency, v is the velocity of the wave, and λ is the wavelength. The velocity of sound in air is approximately 343 m/s. Therefore, the frequency of the sound emitted is 343 m/s / 1.75 mm = 196,000 Hz.

To find the frequency of the sound emitted by the phonograph record, we can use the equation:

v = λ * f

where:
v is the velocity of the wave (in this case the linear velocity of the groove on the phonograph record),
λ is the wavelength of the wave, and
f is the frequency of the wave.

First, we need to find the linear velocity, v.

The linear velocity of the groove on the phonograph record can be calculated using the formula:

v = 2 * π * r * n

where:
r is the distance from the center of the record to the groove (12.7 cm),
n is the revolutions per minute of the record (33 rpm), and
π is a constant (approximately 3.14159).

Now we can calculate v:

v = 2 * π * (12.7 cm) * (33 rpm)
v ≈ 2 * 3.14159 * 12.7 cm * 33 rpm
v ≈ 2 * 3.14159 * 12.7 cm * (33/1) min⁻¹
v ≈ 2 * 3.14159 * 12.7 cm * 33/60 min⁻¹ (since 1 min is equal to 60 seconds)
v ≈ 2 * 3.14159 * 12.7 cm * 11.55 s⁻¹
v ≈ 913.12 cm/s

Now we can solve for the frequency (f):

f = v / λ
f = 913.12 cm/s / 1.75 mm
f = 913.12 cm/s / 0.175 cm
f = 5224 Hz

Therefore, the frequency of the sound emitted by the phonograph record is approximately 5224 Hz.

To find the frequency of the sound emitted, we can use the formula:

Frequency = Speed of sound / Wavelength

First, let's find the speed of sound. The speed of sound in air is around 343 meters per second.

Now, we need to convert the wavelength to meters. Since the given wavelength is in millimeters, we divide it by 1000 to convert it to meters. So, the wavelength is 0.00175 meters.

Now, we can calculate the frequency using the formula:

Frequency = 343 / 0.00175

Frequency ≈ 196000 Hz

Therefore, the frequency of the sound emitted will be approximately 196000 Hz.